Beam test result and digitization of TaichuPix-3: A Monolithic Active Pixel Sensors for CEPC vertex detector

The Circular Electron-Positron Collider (CEPC), as the next-generation electron-positron collider, is tasked with advancing not only Higgs physics but also the discovery of new physics. Achieving these goals requires high-precision measurements of particles. Taichu seires, Monolithic Active Pixel Sensor (MAPS), a key component of the vertex detector for CEPC was designed to meet the CEPC's requirements. For the geometry of vertex detector is long barrel with no endcap, and current silicon lacks a complete digitization model, precise estimation of cluster size particularly causing by particle with large incident angle is needed. Testbeam results were conducted at the Beijing Synchrotron Radiation Facility (BSRF) to evaluate cluster size dependence on different incident angles and threshold settings. Experimental results confirmed that cluster size increases with incident angle. Simulations using the Allpix$^2$ framework replicated experimental trends at small angles but exhibited discrepancies at large angles, suggesting limitations in linear electric field assumptions and sensor thickness approximations. The results from both testbeam and simulations have provided insights into the performance of the TaichuPix chip at large incident angles, offering a crucial foundation for the establishment of a digital model and addressing the estimation of cluster size in the forward region of the long barrel. Furthermore, it offers valuable references for future iterations of TaichuPix, the development of digital models, and the simulation and estimation of the vertex detector's performance.